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Proof step 5 from proof div-twoodd-01 (previous step)

2 ≠ 0 ∧ i - 1 < 0 ⊦ i < 0 ∧ i % 2 = 0 → ~((~ i + 1) / 2) = i / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div2-odd seq: i % 2 = 0, 0 ≤ i ⊦ (i + 1) / 2 = i / 2 subst: [i] → [~ i] flags: rewrite, current

Additional information

Used simplifier rules: mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%Div-left: ⊦ j ≠ 0 → ~ i / j = ~(i / j);%two-even: ⊦ i % 2 = 0 → (i / 2 = j ↔ i = 2 * j);%mult-div-switch: ⊦ j ≠ 0 ∧ i % j = 0 → i / j * j = i;%neg-10: ⊦ ~ i = 0 ↔ i = 0; from specification int-abs%neg-02: ⊦ ~ ~ i = i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2 Used terms: ~ i